ON-LINE BIAS AND FROTH DEPTH MEASUREMENT IN FLOTATION COLUMNS : A PROMISING TOOL FOR AUTOMATIC CONTROL AND REAL-TIME OPTIMIZATION
Jocelyn Bouchard 1 , Master's degree student René del Villar2 , Professor André Desbiens3, Associate-Professor Véronique Aubé4 , Master's degree student LOOP (Laboratoire d'observation et d'optimisation des procédés Process observation and optimization laboratory) Université Laval, Pavillon Adrien-Pouliot, Québec (Québec), Canada, G1K 7P4 1
Department of mining, metallurgical and material engineering PH : (418) 656-2131, ext : 12645 E-mail :
[email protected]
3
Department of mining, metallurgical and materials engineering PH : (418) 656-7487 E-mail :
[email protected] 2
4
Department of electrical and computer engineering, PH: (418) 656-2131, ext: 3408 E-mail :
[email protected]
Department of mining, metallurgical and materials engineering PH : (418) 656-2131, ext : 12645 E-mail :
[email protected]
1 ABSTRACT The metallurgical performance of column flotation is
interface position is important from a metallurgical point of view because it determines the relative importance of the cleaning and the collection zones. In this paper, both
determined by the concentrate grade and recovery. Although the former can be continuously measured using
expressions will be used indiscriminately.
an on-stream analyzer, the latter must be estimated by a material balance calculation based on seldom verified steady-state assumptions. Consequently, the automatic control and optimization of flotation columns should be performed using secondary variables having a strong influence on the metallurgical performance, such as froth depth, gas hold-up or bubble surface area flux and bias.
Many techniques have been proposed in the pas t for froth depth measurement. The most common ones are summarized by Finch and Dobby (1990) and some further developments are presented by Bergh and Yianatos (1993) and del Villar et al. (1995a, 1995b, 1999). All
The aim of this paper is to present a method to get froth depth and bias measurements using virtual sensors. Fractional factorial experiment design for the neural
conductivity, between the pulp and the froth to locate the pulp-froth interface position. Even though the principles behind these methods are fairly simple, some of them
network calibration of the bias sensor, pilot plant results, and eventual industrial applications – including the
have encountered important operating problems that limit their accuracy. Nevertheless, methods based on the use of a float or pressure gages (one to three) are commonly used and seem to be precise enough for day -to-day process supervision.
possibility of achieving effective real-time optimization from bias and froth depth measurements – will also be discussed. INTRODUCTION
New techniques using temperature or conductivity
Flotation columns have been widely studied and used in mineral processing for about twenty years. Although a great deal of work has been accomplished to understand the influence of different variables such as froth depth (H), bubble surface area flux (Sb ) and bias (Jb ) on the metallurgical performance, the measurement of some of these variables is still difficult to be performed – except at the laboratory level – because in most cases, no commercial device yet exists. As a result of this, it is almost impossible to achieve neither efficient control nor optimization of the process at the industrial level, even in open-loop operation with well experienced operators. This paper aims at presenting a new method to get accurate froth depth and bias measurements using virtual sensors based on the conductivity profile along the column upper section. The emphasis is put on the calibration of the bias sensor and the primary pilot plant results. Eventual industrial applications and possibilities measurements are also discussed.
these methods use the difference of a physical characteristic, such as specific gravity, temperature or
of
such
BACKGROUND Froth depth and pulp-froth interface position measurements provide the same information about the flotation column operation. Current measuring methods generally attempt to locate the pulp-froth interface instead of directly measuring the froth depth. The pulp-froth
profiles have shown promising characteristics for industrial applications. Besides being very accurate, the gathered information can also be used for inferring the bias as indicated hereafter. Conductivity profile probes have been successfully tested by Gomez et al. (1989), Bergh and Yianatos (1993) and del Villar et al. (1999). Moreover, important improvements has been introduced since their inception, namely in what concerns the conductivity profile scanning time, which has improved from one minute (Gomez et al., 1989) to less than one second (del Villar et al., 1999). The bias is another important variable for the column flotation process optimization since it is highly correlated to the concentrate grade for a given reagent dosage and Sb . Defined by Finch and Dobby (1990) as “the net downward flow of water through the froth” or by its equivalent “the net difference of water flow between the tailings and feed” (mass balance calculation around the collection zone), the bias can be qualitatively interpreted as the fraction of the wash water flow really useful for froth cleaning. The wash water flow rate is more often used since simpler, but it does not correlate well to the concentrate grade and recovery. In fact, it also includes the fraction of wash water flow short-circuited to the concentrate which is not used for froth cleaning.
2 Accurate bias measurement with common devices (flow meter and density meter) is difficult to achieve because a steady-state assumption has to be made to
performed on a two-phase system (water – air, no solids) and a three-phase system (water – minerals – air). The feed pulp was composed of an iron ore containing
obtain the bias from a mass balance calculation (Finch and Dobby, 1990). Moreover, error propagation resulting
approximately 10 % silicates and a reverse flotation was targeted (silicate flotation). All experiments were
from the use of four instruments (two flow meters and two density meters) to infer a rather small value, leads to high relative standard deviations (Finch and Dobby, 1990).
conducted at 20 % to 30 % solids. Feed conductivity was adjusted using NaCl for the two -phase experiments.
These facts justify the interest of developing an alternative method.
Froth depth measurement
Another approach validated by Uribe-Salas et al. (1991) consists in using a conductivity balance calculation. Known as the "rule of additivity", its final expression is given by :
K ' f − K 't − J 'c K 'c − K w J b = J 't K ' f −K w K ' f −K w
(1)
and involves the knowledge of the tail (J't ) and concentrate (J'c) water flow rates as well as the conductivity of wash water flow (Kw ) and those of the feed (K'f), tail (K' t ), and concentrate (K' c) water flows. This method is rather limited to steady-state laboratory scale tests. Moys and Finch (1988) have reported the existence of a relationship between the bias and the temperature profile along the column. An equivalent relationship between bias and conductivity profile has been introduced by Xu et al. (1989) and later detailed by Uribe-Salas et al. (1991). Pérez and del Villar (1996) have proposed a neural network modeling approach to obtain a mathematical representation of the relationship between the conductivity profile and the bias. The use of this sensor for automatic control have been presented by del Villar et al. (1999) and Milot et al. (2000) for a two-phase laboratory column operation.
The pulp-froth interface position is measured using semi-analytical method based on the conductivity profile along the column developed by Grégoire (1997). As described by Desbiens et al. (1998) and del Villar et al. (1999), this approach replaces the previous search of the inflection point of the conductivity profile using a neural network algorithm, thus eliminating the extensive experimentation required for the training of the neural network. In the current method, the various pairs of electrodes (each pair corresponds to a conductivity cell) are sequentially activated to avoid secondary currents and the corresponding conductivity value is calculated through a very precise electronic circuit. The scanning of the whole set of electrodes takes less than one second. Grégoire’s technique is based on the assumption that the resistance of the cell containing the pulp-froth interface is a weighted average of those immediately above (in the froth zone) and below (in the pulp zone). The measurement is achieved in two steps. First, an algorithm locates the cell containing the interface (highest conductivity change). The actual froth depth is then calculated from the conductivity of this cell and that of the immediately adjacent ones (below and above). Figure 1 compares the sensor measurements to the observed values (in a transparent column). Although Grégoire's algorithm is very accurate, it fails with high conductivity feeds (above 1200 µS/cm). In
instrumented with flow meters for feed, tails, wash water and air as well as with a conductivity profile sensor
these cases, the conductivity profile is very steep below the interface and a larger conductivity change may occur at the bottom of the sensor (near the feed inlet) as compared to that where the interface is really located. This change results from the important difference in conductivity between the feed (above 1200 µS/cm) and
(eleven 11-cm spaced stainless rings) and conductivity cells on the feed and wash water flows. Local control loops are implemented to regulate feed, tails, wash water
the wash water flow rates (between 100 and 200 µS/cm). This problem can be easily solved by taking into account the slope of the conductivity profile before the
and air flow rates. The tests described in this paper were
"discontinuity" in the calculation algorithm. As shown in
EXPERIMENTAL APPARATUS The pilot flotation column used in this work is 7 m height (23’) and 5.25 cm (2’’) diameter. The column is
3 Figure 2, the froth phase conductivity is quite constant so that the absolute value of the slope near the interface tends to infinity.
This black-box modeling approach has the great advantage of providing an easy-to-get and effective model from the experimental data. On the other hand, the model has no physical meaning and is dependant on the network structure, the initial state of the interconnection weights
Measured froth depth (cm)
80
and the experimental data. Moreover, the calibration of neural network requires an extensive experimental program. Nevertheless, the method remains very
70
interesting as it is demonstrated in the following sections. As for froth depth, the bias measurement is completed in less than a second.
60 50 40
BIAS SENSOR CALIBRATION
30 20 20
30
40
50
60
70
80
Observed froth depth (cm)
Figure 1. Froth depth sensor performance.
effects (i.e. effects of a single variable or combined effects of small group of variables) is avoided. To cover a wide range of experimental conditions with the fewest
1 10
2
20 True Interface position
Cells
4 5 6
Conductivity change caused by the difference of conductivity between the feed and wash water flows
7
30 40 50 60
Froth depth (cm)
3
70
8
80
9
90
10
The effectiveness of the bias sensor depends on the richness of the information present in the experimental data. Therefore, it is essential to carefully program the experiments to ensure that the information is well structured, diversified and that confusion between main
100 Conductivity ( µS/cm)
Figure 2. Froth depth sensor limitation.
For the operation with a three-phase system, similar results were obtained. However, the reliability of the measurements seem compromised when the electrodes clogged-up after a few hours of operation. In those cases, errors of about 5 cm were experienced. More tests are being conducted in different operating conditions to evaluate the evolution of the error in time and to study how it can be avoided. Bias measurement Bias measurement is achieved using the neural network modeling technique developed by Pérez and del
number of tests, a fractional factorial experimental design has been chosen. The five chosen factors for a two-phase system (only water and air, no solids) are: the air (J g ), feed (Jf) and wash water flow rates (Jw ), the froth depth (H) and the feed conductivity (Kf). A three-level factorial design has been used instead of a two level design to provide a better precision for the sensor and a better use of the neural network nonlinear modeling capabilities. With a full design, this factor-level combination have led to a 243test program (35). Seeking a more reasonable number of experiments, a half-fraction design was chosen and only 81 (3(5-1)) different tests were programmed. The levels for each factor are shown in Table 1. For the half-fraction design, only the treatments involving feed flow rate high level remain in the set of tests. For each experiment, the column was maintained in steady -state during a three residence time period before proceeding to the required measurements (conductivities and flow rates). Obviously, this reduction in the number of experiments will affect the resolution of the design (i.e.
Villar (1996). The only “physical” measurements required are those made by the froth depth probe, some flow rates
the capacity of discerning the effect of single variables or combined variables). Skipping the details of the resolution calculation (Mason et al., 1989), let’s just say that for a
and the conductivities of the feed and wash water flows.
five-factor and three-level
half-fraction
design,
no
4 confusion should be expected between single variable effects and four-variable (or less) combined effects, as well as between two -variable combined effects and threevariable (or less) effects. Consequently, the design should be able to provide a sufficient precision since it is generally admitted that most of the information comes from low order interactions (single variables or small group of variables).
RESULTS FOR A THREE-PHASE SYSTEM The sensor, calibrated with the two-phase data, was then tested in the same flotation column using this time a mineral pulp feed. The purpose of these tests is to evaluate the possibility of using a water-only calibration, which is easier to perform than a pulp-based calibration, for bias measurement in an industrial scale column. The four chosen factors for a three-phase system are: the air (Jg ), feed (Jf) and wash water flow rates (Jw ) and the froth depth (H). The chosen levels for each factor are shown at
Table 1.
Two-phase system factor levels
Jf (cm/sec)
Jw (cm/sec)
Jg (cm/sec)
H (cm)
Kf (µS/cm)
+1
1
0,3
1,2
65
1300
0
0,8
0,2
1
50
800
-1
0,6
0,1
0,8
35
300
Table 2 and once again, only the treatments involving feed flow rate high level are considered. Unfortunately, the extrapolation to a pulp feed is not satisfactory. As presented at Figure 4, preliminary results show practically no correlation between the calculated values (mass and conductivity balance calculation) and the measurement predicted by the sensor.
The validation of neural network model for the twoTable 2.
phase system was accomplished using a new data set composed of 17 repeated tests of the original design. Figure 3 compares the predictions made by the sensor and the "reconciled" values of the calibration and validation data sets. It can be seen that the sensor may be really effective when used within its calibration range. The reconciled reference bias was obtained from mass and
observation window). 0,20
measured bias (cm/s)
0,15
Jf (cm/sec)
Jw (cm/sec)
Jg (cm/sec)
H (cm)
+1
1
0,3
1,2
65
0
0,8
0,2
1
50
-1
0,6
0,1
0,8
35
0,05 0,04
measured bias (cm/s)
conductivity balance calculations. The data reconciliation was achieved using the flow rates and conductivity measurements (mean values for a 10-minute steady state
Three-phase system factor levels
0,03 0,02 0,01 0 -0,01 -0,02
0,10
-0,03 -0,04
0,05
0 -0,05
0,00 -0,05
0,1
0,15
0,2
0,25
0,3
calculated bias (cm/s)
0,00 -0,10
0,05
0,05
0,10
0,15
0,20
Validation data Calibration data prediction = calculated value
Figure 4. Bias sensor performance for the three-phase system (two-phase calibration).
-0,10
calculated bias (cm/s)
Figure 3. Bias sensor performance.
This lack of robustness may probably be explained by the great difference in the conductivity profile between the experiments conducted with the two-phase system, for the sensor calibration, and those conducted with the three-
5 phase system. In such a case, the systems would behave quite differently and the extrapolation outside the calibration range becomes risky. Figure 5 shows the
such device in an industrial column could significantly improve the understanding of the relationship between bias and froth depth and the column metallurgical
conductivity profiles for tests conducted with water-only and with pulp using the same operating conditions. The
performance. This could lead to great possibilities for inplant optimization of the flotation column process.
observed difference can be explained by the greater stability of the froth in the three-phase system. In fact for the latter case, the mass balance calculations around the froth zone has revealed that very little water from the feed flow is driven to the concentrate as compared to the twophase case. The stability of the froth thus favors greater bias values than those the neural network is trained to detect. Nevertheless, since conductivity profile shapes are similar for both systems (pulp and water), results as good as those obtained with the water-only system should be expected with pulp as long as the neural network is calibrated directly with pulp or under froth conditions (water-only system) similar to those encountered with the pulp. New tests are currently undergoing to confirm this hypothesis. 120
froth
two-phase
height (cm)
100
three-phase
80
pulp or water
60 40
If we consider a step further in the improvement of the process control, bias and froth depth measurements could establish the basis to support a hierarchical control strategy. Since flotation columns are often overdimensioned and consequently, less affected by external perturbations, it is legitimate to question the interest of implementing such a strategy. The answer could be found in the interest of industries to improve their metallurgical performance, to increase productivity and to decrease production costs, targets difficult to reconcile with the current control practice. In fact, this one generally rely on insufficient information about critical operating variables (besides froth depth) and a choice of set points rather based on intuition and operating easiness instead of technical considerations. Figure 6 illustrates the principle of a hierarchical control strategy applied to column flotation. After the regulation of all flow rates (tertiary variables) with local SISO control loops, the following step is the control of secondary variables (bias, froth depth and Sb ) having a strong influence on the metallurgical performance. At this stage, it might be necessary to implement a multivariable controller that allows to reach and maintain secondary variable set points (stabilizing control). Such a structure
20 0 0
50
100
150
200
250
300
conductivity (µS/cm)
Figure 5. Conductivity profile for the two-phase and threephase system.
EVENTUAL INDUSTRIAL APPLICATIONS The conductivity-based froth depth probe has shown to be very accurate, fast and robust. It requires lowmaintenance and has a very low cost. Although the results with a three-phase system are not successful at the time this article was written, previous tests (Pérez-Garibay and del Villar, 1997) have indicated that the same probe can provide good estimates of the bias, a variable which is not measured by any existing device. The implementation of
has been successfully tested for bias and froth depth control by Milot et al. (2000) and del Villar et al. (1999) for a two-phase laboratory-scale operation. Tests using a three-phase system (water, air and minerals) on a pilot unit are currently being conducted at Laval University. Time scale
Type of control
hour or day
Primary variables: grade & recovery
Real-time optimization multivariable
minute
Secondary variables: froth depth, bias, gas holdup, Sb
Stabilizing monovariable & multivariable
second
Tertiary variables: feed, wash water, concentrate, tail and gas flow rates
Local loops monovariable
Figure 6. Hierarchical control strategy applied to column flotation.
6 Set points of the secondary variables control loops could be either fixed manually or by an on-line optimization algorithm (real-time optimization) to obtain
Del Villar, R., Pérez and R., Diaz, G., 1995b, "Improving the three-pressure transducer method of level detection in flotation columns", Proceedings of Copper 95
the desired concentrate grade and recovery for some given production objectives in term of productivity or
– Cobre 95 International conference, pp. 247-260.
production costs. In both cases, the relationship between the secondary variables and the metallurgical performance must be known.
Del Villar, R, Grégoire, M. and Pomerleau, A., 1999, " Automatic control of a laboratory flotation column ", Minerals Engineering, Vol. 12, No. 3, pp. 291-308.
As previously mentioned, the bubble surface area flux
Desbiens, A., del Villar, R. and Milot, M., 1998,
(Sb ) is another key variable for the flotation metallurgical performance (Gorain et al., 1996, Heiskanen, 2000).
"Identification and Gain-Scheduled Control of a Pilot Flotation Column", International Federation of Automatic Control (IFAC) Symposium on Automation in Mining, Mineral and Metal Processing, Cologne, pp. 337-342.
Successful estimation of Sb using a conductivity probe for gas hold-up measurements and the drift flux analysis (Dobby et al., 1988) for bubble diameter estimation has been achieved for a lab-scale column (Li et al, 2001). Such a device will be soon be integrated to the experimental set-up to evaluate the potential of this variable for metallurgical control purposes.
Dobby, G.S., Yianatos, J.B. and Finch, J.A., 1988, "Estimation of Bubble Diameter in Flotation Columns From Drift Flux Analysis", Canadian Metallurgical Quarterly, Canadian Institute of Mining and Metallurgy, Pergamon Press, Vol. 27, No. 2, pp. 85-90.
CONCLUSION The froth depth and bias sensors based on the conductivity profile along the upper section of a flotation column have undoubtedly an interesting potential to improve the understanding of the process and to facilitate its optimization. Until then, the robustness of the sensor must be improved regarding the type of feed, froth and column scale.
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ACKNOWLEDGEMENTS The authors wish to thank NSERC (Natural Science
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